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Piatnitski, Andrey Lvovich

Statistics Math-Net.Ru
Total publications: 16
Scientific articles: 13
Presentations: 19

Number of views:
This page:1245
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Senior Researcher
Doctor of physico-mathematical sciences, Doctor of technical sciences (2016)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 21.12.1955
Phone: +7 (499) 133 22 18
E-mail: ,
Website: http://fian-pages.lebedev.ru/andrey
Keywords: homohenization, stochastic homogenization, Gamma-convergence, singular perturbation.
UDC: 517.956.226, 517.9, 517.946

Subject:

Homogenization, stochastic homogenization, singularly perturbed operators, Gamma-convergence, behaviour of solutions at infinity.

   
Main publications:
  • Kozlov, S.M.; Piatnitski, A.L. Effective diffusion for a parabolic operator with periodic potential. SIAM J. Appl. Math. 53, No. 2, 401–418 (1993).
  • Kozlov, S.M.; Piatnitski, A.L. Degeneration of effective diffusion in the presence of periodic potential. Ann. Inst. Henri Poincare, Probab. Stat. 32, No. 5, 571–587 (1997).
  • Piatnitski, A.L. Asymptotic behavior of the ground state of singularly perturbed elliptic equations. Commun. Math. Phys. 197, No. 3, 527–551 (1998).
  • Chechkin, G.A.; Friedman, A. ; Piatnitski, A.L. The boundary-value problem in domains with very rapidly oscillating boundary. J. Math. Anal. Appl. 231, No. 1, 213–234 (1999).
  • Piatnitski, A.; Remy, E. Homogenization of Elliptic Difference Operators. SIAM J. Math. Analysis 33, No. 1, 53–83, (2001).
  • Allaire, G.; Piatnitski, A. Uniform spectral asymptotics for singularly perturbed locally periodic operators. Communications in Partial Differential Equations 27, No. 3-4, 705–725, (2002).
  • Kleptsyna, M.L.; Piatnitski, A.L. Homogenization of Random Nonstationary Convection-Diffusion Problem. Russian Mathematical Surveys, 57, No. 4, 729–751, (2002).
  • Bourgeat, A.; Jurak, M.; Piatnitski A.L. Averaging a transport equation with small diffusion and oscillating velocity. Mathematical Methods in the Applied Sciences, 26, No. 2, 95–117, (2003).
  • Pardoux, E.; Piatnitski A. Homogenization of a nonlinear random parabolic partial differential equation. Stochastic Processes and their Applications, 104, No. 1, 1–27, (2003).
  • Allaire, G.; Capdeboscq, Y.; Piatnitski, A.L. Homogenization and localization with an interface. Indiana Univ. Math. J. 52, No. 6, 1413–1446, (2003).
  • Bourgeat, A.; Mikelic, A.; Piatnitski, A. On the double porosity model of a single phase flow in random media. Asymptotic Analysis 34, No. 2, 311–332, (2003).
  • Cioranescu, D.; Piatnitski, A. Homogenization in perforated domains with rapidly pulsing perforations. ESAIM: Control, Optimisation and Calculus of Variations 9, 461–484, (2003).
  • Bourgeat, A.; Piatnitski, A. Approximations of effective coefficients in stochastic homogenization. Ann. Inst. H. Poincare, Prob. Statistics 40, No. 2, 153–165, (2004).
  • Piatnitski, A.; Shamaev, A. On the Asymptotic Behavior of Eigenvalues and Eigenfunctions of Non-Self-Adjoint Elliptic Operators. Journal of Mathematical Sciences 120, No. 3, 1411–1423, (2004).
  • Braides, A.; Chiado Piat, V.; Piatnitski, A. A variational approach to double-porosity problems. Asymptotic Analysis 39, No. 3-4, 281–308, (2004).
  • Allaire, G.; Capdeboscq, Y.; Piatnitski, A. Siess, V.; Vannitathan, M. Homogenization of Periodic Systems with Large Potentials. Arch. Rational Mech. Anal. 174, 179–220, (2004).
  • Allaire, G.; Piatnitski, A. Homogenization of the Schredinger Equation and Effective Mass Theorems. Comm. Math. Physics 258, 1–22, (2005).
  • Marusic-Paloka, E.; Piatnitski, A. Homogenization of a nonlinear convection-diffusion equation with rapidly oscillating coefficients and strong convection. Journal of London Math. Soc. 72, No. 2, 391–409 (2005).
  • Diop, M. ; Iftimie, B.; Pardoux, E.; Piatnitski, A. Singular homogenization with stationary in time and periodic in space coefficients. Journal of Functional Analysis 231, No. 1, 1–46 (2006).
  • Cioranescu, D.; Piatnitski, A. Homogenization of a porous medium with randomly pulsating microstructure. Multiscale Modeling & Simulation 5, No. 1, 170–183 (2006).
  • Zhikov, V.V.; Piatnitski, A.L. Homogenization of random singular structures and random measures. Izvestiya: Mathematics 70, No. 1, 19–67 (2006).
  • Piatnitski, A.L. Homogenization of random nonstationary parabolic operators. Topics on Concentration Phenomena and Problems with Multiple Scales, A. Braides and V. Chiado Piat (Eds.) Lecture Notes of the Unione Matematica Italiana, 2.

http://www.mathnet.ru/eng/person11017
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https://mathscinet.ams.org/mathscinet/MRAuthorID/209790
http://orcid.org/0000-0002-9874-6227

Publications in Math-Net.Ru
2019
1. E. A. Zhizhina, A. L. Piatnitski, “On the behaviour at infinity of solutions to nonlocal parabolic type problems”, The Bulletin of Irkutsk State University. Series Mathematics, 30 (2019),  99–113  mathnet  isi
2018
2. R. R. Gadyl'shin, A. L. Piatnitski, G. A. Chechkin, “On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type”, Izv. RAN. Ser. Mat., 82:6 (2018),  37–64  mathnet  elib; Izv. Math., 82:6 (2018), 1108–1135  isi  scopus
2006
3. V. V. Zhikov, A. L. Piatnitski, “Homogenization of random singular structures and random measures”, Izv. RAN. Ser. Mat., 70:1 (2006),  23–74  mathnet  mathscinet  zmath  elib; Izv. Math., 70:1 (2006), 19–67  isi  elib  scopus
2002
4. M. L. Kleptsyna, A. L. Piatnitski, “Homogenization of a random non-stationary convection-diffusion problem”, Uspekhi Mat. Nauk, 57:4(346) (2002),  95–118  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 57:4 (2002), 729–751  isi  scopus
5. S. B. Kuksin, N. S. Nadirashvili, A. L. Piatnitski, “Hölder estimates for solutions of parabolic SPDEs”, Teor. Veroyatnost. i Primenen., 47:1 (2002),  152–159  mathnet  mathscinet  zmath; Theory Probab. Appl., 47:1 (2003), 157–163  isi
2001
6. A. G. Belyaev, A. L. Piatnitski, G. A. Chechkin, “Averaging in a perforated domain with an oscillating third boundary condition”, Mat. Sb., 192:7 (2001),  3–20  mathnet  mathscinet  zmath  elib; Sb. Math., 192:7 (2001), 933–949  isi  scopus
1998
7. A. G. Belyaev, A. L. Piatnitski, G. A. Chechkin, “Asymptotic behavior of the solution of a boundary value problem in a punctured domain with an oscillating boundary”, Sibirsk. Mat. Zh., 39:4 (1998),  730–754  mathnet  mathscinet  zmath; Siberian Math. J., 39:4 (1998), 621–644  isi
1990
8. S. M. Kozlov, A. L. Piatnitski, “Averaging on a background of vanishing viscosity”, Mat. Sb., 181:6 (1990),  813–832  mathnet  mathscinet  zmath; Math. USSR-Sb., 70:1 (1991), 241–261  isi
1983
9. A. L. Piatnitski, “Averaging a singularly perturbed equation with rapidly oscillating coefficients in a layer”, Mat. Sb. (N.S.), 121(163):1(5) (1983),  18–39  mathnet  mathscinet  zmath; Math. USSR-Sb., 49:1 (1984), 19–40
1982
10. A. L. Piatnitski, “On the behaviour at infinity of the solution of a second-order elliptic equation given on a cylinder”, Uspekhi Mat. Nauk, 37:2(224) (1982),  231–232  mathnet  mathscinet  zmath; Russian Math. Surveys, 37:2 (1982), 249–250  isi
1981
11. A. L. Piatnitski, “Propagation of a solution of a hyperbolic equation with rapidly oscillating coefficients”, Uspekhi Mat. Nauk, 36:1(217) (1981),  223–224  mathnet  mathscinet  zmath; Russian Math. Surveys, 36:1 (1981), 250–251  isi
12. A. L. Piatnitski, “A scattering problem in laminar media”, Mat. Sb. (N.S.), 115(157):3(7) (1981),  478–492  mathnet  mathscinet  zmath; Math. USSR-Sb., 43:3 (1982), 427–441
13. A. L. Piatnitski, “On the limit behavior of the domain of dependence of a hyperbolic equation with rapidly oscillating coefficients”, Mat. Sb. (N.S.), 115(157):1(5) (1981),  130–145  mathnet  mathscinet  zmath; Math. USSR-Sb., 43:1 (1982), 117–131

2018
14. Yu. A. Alkhutov, I. V. Astashova, V. I. Bogachev, V. N. Denisov, V. V. Kozlov, S. E. Pastukhova, A. L. Piatnitski, V. A. Sadovnichii, A. M. Stepin, A. S. Shamaev, A. A. Shkalikov, “Vasilii Vasil'evich Zhikov (obituary)”, Uspekhi Mat. Nauk, 73:3(441) (2018),  169–176  mathnet  elib; Russian Math. Surveys, 73:3 (2018), 533–542  isi
2016
15. C. Wayne, T. Kappeler, G. Kokarev, W. Craig, A. Piatnitsky, I. Chueshov, A. Shirikyan, L. H. Eliasson, “Sergei Borisovich Kuksin (on his 60th birthday)”, Uspekhi Mat. Nauk, 71:1(427) (2016),  177–183  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 71:1 (2016), 167–173  isi
1996
16. N. S. Bakhvalov, A. Yu. Belyaev, M. I. Vishik, V. V. Zhikov, V. P. Maslov, O. A. Oleinik, G. P. Panasenko, A. L. Piatnitski, “Sergei Mikhailovich Kozlov (obituary)”, Uspekhi Mat. Nauk, 51:4(310) (1996),  145–146  mathnet  mathscinet; Russian Math. Surveys, 51:4 (1996), 723–725  isi

Presentations in Math-Net.Ru
1. Вариационные методы в нелокальных задачах усреднения
A. L. Piatnitski
Differential equations, analysis and control: theory and applications
November 18, 2019 18:30
2. Усреднение тонкого периодического сита Стеклова
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
August 20, 2019 16:00
3. Периодическое усреднение нелокальных операторов свёрточного типа
A. L. Piatnitski
Differential equations, analysis and control: theory and applications
March 25, 2019 18:30
4. Усреднение параболического уравнения для несимметричных нелокальных операторов с периодическим ядром
E. A. Zhizhina, A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
February 12, 2019 16:00
5. Предельные теоремы для аддитивных функционалов от диффузионных процессов в случайных средах. (продолжение доклада от 16 октября)
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
November 6, 2018 16:00
6. О некоторых результатах В.В. Жикова в теории усреднения
A. L. Piatnitski
Dynamical systems and differential equations
October 22, 2018 18:30
7. Предельные теоремы для аддитивных функционалов от диффузионных процессов в случайных средах
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
October 16, 2018 16:00
8. Усреднение сингулярных мер и структур
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
June 20, 2017 16:00
9. Стохастическое усреднение
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
June 6, 2017 16:00
10. Усреднение интегральных операторов
E. A. Zhizhina, A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
November 15, 2016 16:00
11. Предельные теоремы для симметричного случайного блуждания в высоко-контрастной периодической среде
A. L. Piatnitski, E. A. Zhizhina
Dobrushin Mathematics Laboratory Seminar
October 18, 2016 16:00
12. Усреднение уравнения типа Навье-Стокса для электро-реологической жидкости в случайной среде
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
July 26, 2016 16:00
13. Дискретные модели двойной пористости
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
April 5, 2016 16:00
14. О законе больших чисел для эллиптического i.i.d. случайого блуждания на целочисленной решетке
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
February 2, 2016 16:00
15. Соотношение Эйнштейна для диффузии в случайной среде
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
November 10, 2015 16:00
16. Усреднение низкотемпературных спиновых систем со случайными коэффициентами взаимодействия
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
July 28, 2015 16:00
17. Homogenization of discrete double porosity models
A. L. Piatnitski
International Conference on Differential Equations and Dynamical Systems
July 5, 2014 09:45
18. Homogenization of spin energies
A. L. Piatnitski
Sixth International Conference on Differential and Functional Differential Equations DFDE-2011
August 16, 2011 12:55   
19. Einstein relation for random walks in random environments
A. L. Piatnitski
Dobrushin Mathematics Laboratory Seminar
August 2, 2011 16:00

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